The Character Challenge system makes its first appearance in Hyperdimension Neptunia Victory. Character Challenges give characters stat increases and other bonuses for completing the requisites.
There are 8 levels for each challenge and once your character fulfills the required conditions for that level of the challenge a dialogue box will appear in the upper right hand corner of the screen to notify you of the challenge and level you have completed as well as the reward for completing it.
Challenges can range from conditions that have to be met in battle such as fleeing or killing a number of enemies or can even be related to the on-screen character the player is currently using.
i.e.: The Player is using Neptune as the party leader and jumps 10 times while she is the on-screen character. This will get Neptune the the reward for the "I Love Gravity Lv.1" challenge. If the player makes Noire the party leader and preforms the same action, she will get the same achievement.